First off, those engine temperatures look to be in degrees F, not C. An engine running at 195 degC (380+ degF) would be toast. Warped heads, etc.
I've generally seen the recommended transmission fluid temperature is less than 200 degF. Cooler temperatures mean longer fluid life and longer transmission life. Operating over 200 degF starts to shorten the fluid life. The transmission would still be fine as long as the fluid is changed sooner. But going over 240-250 degF is likely destructive for both, the fluid and transmission.
The temperatures you posted for your transmission look reasonable in degC. 200 degF is about 94 degC.
My opinion: if you're seeing transmission temperatures over 94 degC, then get an auxiliary cooler as it'll help prolong your transmission. If the temperatures remain lower than 94 degC, then don't bother with another cooler cuz the factory setup is cooling sufficiently.
*Disclaimer: I'm only sharing my opinion. You didn't pay for it, so my opinion is only worth that much, haha.<br />2013 GMC Terrain SLT-1, FWD, 3.6 V6 (LFX), Sunroof